Multi-stage DC-DC converter

ABSTRACT

A multi-stage DC-DC converter is provided that utilizes multiple loops in the control system to perform stable operation. The multi-stage DC-DC converter includes: a first DC-DC converter, a second DC-DC converter provided as a latter stage to said first DC-DC converter and a control circuit that controls the switching operation performed by said first DC-DC converter based on at least the output voltage of said first DC-DC converter and the output voltage of said second DC-DC converter. Since the control system is formed with an external loop for feedback of the output voltage of the second DC-DC converter and an internal loop for feedback of the output voltage of the first DC-DC converter, the resonance frequencies on the low-frequency side in the transfer function of the entire control system are shifted to higher frequencies than in the case where the control system consists of a single loop, even in cases where stabilization of the control system is difficult with single-loop output voltage feedback control. Accordingly, the frequency at which the phase crosses zero degrees is becomes higher, so the gain margin increases and the operation of the control system can be stabilized.

BACKGROUND OF THE INVENTION

[0001] The present invention relates to a multi-stage DC-DC converterwherein a plurality of converters is connected in series, andparticularly to a multi-stage DC-DC converter wherein control of theoutput voltage is performed by means of negative feedback of the outputvoltage.

DESCRIPTION OF THE PRIOR ART

[0002] In recent years, DC-DC converters used for communication havelower output voltages and higher currents and, accordingly, improvingefficiency is even more important than previously. To this end,techniques of increasing efficiency by connecting two converters inseries have attracted attention. Such DC-DC converters are calledtwo-stage DC-DC converters.

[0003] Known methods of controlling two-stage DC-DC converters include amethod of achieving stability of operation by optimizing the values ofthe inductors and capacitors within the converters and also theequivalent series resistance values of capacitors (see P. Alou et al.;“Buck+Half Bridge (d=50%) Topology Applied to Very Low Voltage PowerConverters,” IEEE Applied Power Electronics Conference (APEC) 2001).

[0004] In this method, specifically, the resonance frequencies of theinductors and capacitors of the first stage and second stage areseparated from each other and the values of the equivalent seriescircuits are enlarged to achieve stable operation of the control system.

[0005] However, when a two-stage DC-DC converter is manufactured as anactual product, because of limitations with respect to the shape andmounting surface area, it is difficult to use inductors and capacitorsthat are optimal for control. In addition, because of standards for theoutput ripple voltage, it is difficult to increase the equivalent seriesresistance value of capacitors.

[0006] In addition, with a single-stage DC-DC converter, there are knownmethods of achieving stable operation of the control system usingmultiple loops, but with two-stage DC-DC converters, there are manyunknown areas with respect to what kind of multiple-loop scheme can beused to achieve stability of operation of the control system. This pointis the same for DC-DC converters wherein three or more converters areconnected in series.

SUMMARY OF THE INVENTION

[0007] It is therefore an object of the present invention to provide amulti-stage DC-DC converter that uses multiple loops in the controlsystem and that can achieve stable operation.

[0008] In addition, another object of the present invention is toprovide a multi-stage DC-DC converter with a simple construction thatachieves stability by means of a multiple-loop control system even incases wherein stabilization of the control system is difficult withsingle-loop output voltage feedback control.

[0009] In order to solve the aforementioned problem, a multi-stage DC-DCconverter was analyzed by means of state-space averaging, and stateequations were derived so that stable control can be performed based ona multiple loops.

[0010] Specifically, a multi-stage DC-DC converter as one aspect of thepresent invention is a multi-stage DC-DC converter comprising: anon-isolated DC-DC converter that is able to adjust the intermediatevoltage by PWM control as the first stage, an isolated DC-DC converteras the second stage and a PWM controller that controls the duty cycle ofswitching of the first stage by means of negative feedback of the outputvoltage of the second-stage converter, characterized in that theintermediate voltage of the first-stage converter is provided asnegative feedback to the PWM controller.

[0011] Here, in a preferred embodiment of the present invention, theintermediate voltage is provided as negative feedback to the PWMcontroller via an operational amplifier.

[0012] With this configuration, the input voltage is converted to pulsesby the switching of the PWM controller in the first-stage converter andalso, the intermediate voltage is adjusted based on the duty cycle ofswitching, and moreover voltage conversion is performed at thetransformer winding ratio in the second-stage converter, thus generatingan averaged output voltage.

[0013] In this case, not only is the output voltage of the second-stageconverter provided as negative feedback to the PWM controller via anexternal loop, but the intermediate voltage of the first-stage converteris also provided as negative feedback via an internal loop.

[0014] Thereby, compared with the case of an external loop alone, theresonance frequency on the low-frequency side in the transfer functionof the entire control system is shifted to a higher frequency andaccordingly, the frequency at which the phase crosses zero degrees alsobecomes higher. Accordingly, the gain margin is increased and theoperation of the control system is stabilized.

[0015] In addition, a multi-stage DC-DC converter as another aspect ofthe present invention is a two-stage DC-DC converter comprising: anon-isolated DC-DC converter that is able to adjust the intermediatevoltage by PWM control as the first stage, an isolated DC-DC converteras the second stage and a PWM controller that controls the duty cycle ofswitching of the first stage by means of negative feedback of the outputvoltage of the second-stage converter, characterized in that theintermediate voltage of the first-stage converter is provided aspositive feedback to the PWM controller.

[0016] With this configuration, the input voltage is converted to pulsesby the switching of the PWM controller in the first-stage converter andalso, the intermediate voltage is adjusted based on the duty cycle ofswitching, and moreover voltage conversion is performed at thetransformer winding ratio in the second-stage converter, thus generatingan averaged output voltage.

[0017] In this case, not only is the output voltage of the second-stageconverter provided as negative feedback to the PWM controller via anexternal loop, but the intermediate voltage of the first-stage converteris also provided as positive feedback via an internal loop.

[0018] Thereby, compared with the case of an external loop alone, theresonance peak on the low-frequency side in the transfer function of theentire control system vanishes and accordingly, the frequency at whichthe phase crosses zero degrees also becomes much higher. Accordingly,the gain margin is increased considerably and the operation of thecontrol system is even more stabilized.

[0019] In addition, a multi-stage DC-DC converter as still anotheraspect of the present invention is a two-stage DC-DC convertercomprising: a non-isolated DC-DC converter that is able to adjust theintermediate voltage by PWM control as the first stage, an isolatedDC-DC converter as the second stage and a PWM controller that controlsthe duty cycle of switching of the first stage by means of negativefeedback of the output voltage of the second-stage converter,characterized in that the switching current of the first-stage converteris provided as feedback to the PWM controller.

[0020] With this configuration, the input voltage is converted to pulsesby the switching of the PWM controller in the first-stage converter andalso, the intermediate voltage is adjusted based on the duty cycle ofswitching, and moreover voltage conversion is performed at thetransformer winding ratio in the second-stage converter, thus generatingan averaged output voltage.

[0021] In this case, not only is the output voltage of the second-stageconverter provided as negative feedback to the PVVM controller via anexternal loop, but the switching current of the first-stage converter isalso provided instead of a reference signal via an internal loop.

[0022] Thereby, compared with the case of an external loop alone, theresonance frequency on the low-frequency side in the transfer functionof the entire control system vanishes and becomes an inflection pointand accordingly, fourth order delay becomes third order delay.Accordingly, the gain margin is further increased and the operation ofthe control system is even more stabilized.

[0023] In addition, a multi-stage DC-DC converter as still anotheraspect of the present invention is a two-stage DC-DC convertercomprising: a non-isolated DC-DC converter that is able to adjust theintermediate voltage by PWM control as the first stage, an isolatedDC-DC converter as the second stage and a PWM controller that controlsthe duty cycle of switching of the first stage by means of negativefeedback of the output voltage of the second-stage converter,characterized in that the current flowing through the second-stageconverter is provided as feedback to the PWM controller.

[0024] With this configuration, the input voltage is converted to pulsesby the switching of the PWM controller in the first-stage converter andalso, the intermediate voltage is adjusted based on the duty cycle ofswitching, and moreover voltage conversion is performed at thetransformer winding ratio in the second-stage converter, thus generatingan averaged output voltage.

[0025] In this case, not only is the output voltage of the second-stageconverter provided as negative feedback to the PWM controller via anexternal loop, but the current flowing through the second-stageconverter, e.g. the output inductor current, is also provided instead ofa reference signal via an internal loop.

[0026] Thereby, compared with the case of an external loop alone, thephase in the transfer function of the entire control system no longercrosses zero degrees. Accordingly, the operation of the control systemis constantly stabilized.

[0027] Note that in the present invention, “multi-stage” refers to wheretwo or more converters are connected in series.

BRIEF DESCRIPTION OF THE DRAWINGS

[0028]FIG. 1 is a circuit diagram showing the main circuit of atwo-stage DC-DC converter.

[0029]FIG. 2 is a waveform chart showing the operation of the maincircuit 1 of the two-stage DC-DC converter shown in FIG. 1.

[0030]FIG. 3 is an equivalent circuit model of the main circuit 1 of thetwo-stage DC-DC converter shown in FIG. 1.

[0031]FIG. 4 is a circuit diagram showing a two-stage DC-DC converterthat uses single-loop output voltage feedback control.

[0032]FIG. 5 is a block diagram showing the control system for thetwo-stage DC-DC converter 5 shown in FIG. 4.

[0033]FIG. 6 is a graph showing the resonance frequency of the two-stageDC-DC converter 5 shown in FIG. 4.

[0034]FIG. 7 presents Bode plots showing the frequency response of thetwo-stage DC-DC converter 5 shown in FIG. 4, where (a) is a Bode plotshowing the gain as a function of frequency, while (b) is a Bode plotshowing the phase as a function of frequency.

[0035]FIG. 8 is a circuit diagram showing the two-stage DC-DC converteraccording to Preferred Embodiment 1 of the present invention.

[0036]FIG. 9 is a block diagram showing the essential parts of thetwo-stage DC-DC converter 10 shown in FIG. 8.

[0037]FIG. 10 is a block diagram showing the control system of thetwo-stage DC-DC converter 10 shown in FIG. 8.

[0038]FIG. 11 presents Bode plots showing the frequency response of thetwo-stage DC-DC converter 10 shown in FIG. 8, where (a) is a Bode plotshowing the gain as a function of frequency, while (b) is a Bode plotshowing the phase as a function of frequency.

[0039]FIG. 12 is a circuit diagram showing the two-stage DC-DC converteraccording to Preferred Embodiment 2 of the present invention.

[0040]FIG. 13 is a block diagram showing the control system of thetwo-stage DC-DC converter 20 shown in FIG. 12.

[0041]FIG. 14 presents Bode plots showing the frequency response of thetwo-stage DC-DC converter 20 shown in FIG. 12, where (a) is a Bode plotshowing the gain as a function of frequency, while (b) is a Bode plotshowing the phase as a function of frequency.

[0042]FIG. 15 is a circuit diagram showing the two-stage DC-DC converteraccording to Preferred Embodiment 3 of the present invention.

[0043]FIG. 16 is a block diagram showing the control system of thetwo-stage DC-DC converter 30 shown in FIG. 15.

[0044]FIG. 17 presents Bode plots showing the frequency response of thetwo-stage DC-DC converter 30 shown in FIG. 15, where (a) is a Bode plotshowing the gain as a function of frequency, while (b) is a Bode plotshowing the phase as a function of frequency.

[0045]FIG. 18 is a circuit diagram showing the two-stage DC-DC converteraccording to Preferred Embodiment 4 of the present invention.

[0046]FIG. 19 is a block diagram showing the control system of thetwo-stage DC-DC converter 40 shown in FIG. 18.

[0047]FIG. 20 presents Bode plots showing the frequency response of thetwo-stage DC-DC converter 40 shown in FIG. 18, where (a) is a Bode plotshowing the gain as a function of frequency, while (b) is a Bode plotshowing the phase as a function of frequency.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0048] First, in order to demonstrate the advantage of the presentinvention, before describing the multi-stage DC-DC converters accordingto preferred embodiments of the invention in detail, we shall describethe basic circuit structure of the multi-stage DC-DC converter and theproblems that occur when output voltage feedback control is performedwith a single loop.

[0049]FIG. 1 is a circuit diagram showing the main circuit of atwo-stage DC-DC converter which is one type of multi-stage DC-DCconverter.

[0050] As shown in FIG. 1, the main circuit 1 of the two-stage DC-DCconverter consists of a non-isolated converter 2 as the first stage andan isolated converter 3 as the second stage.

[0051] The aforementioned first-stage converter 2 is constructed as aso-called “buck” PWM regulation block, consisting of two switchingtransistors (FETs) Q1 and Q2 that perform pulse width control byswitching based on the PWM controller (not shown) and an inductor Lb′and capacitor Cb′ that perform pulse averaging.

[0052] Moreover, by means of the switching of the aforementioned PWMcontroller, the intermediate voltage V_(b) is kept constant despitefluctuations in the input voltage V_(i) and load R. Note that the inputcapacitor C_(i) contained in the first-stage converter 2 is a capacitorfor stabilizing the input voltage V_(i).

[0053] In addition, the second-stage converter 3 is constructed as aso-called “half bridge” type, consisting of two switching transistors Q3and Q4 that take the intermediate voltage V_(b) from the first-stageconverter 2 and convert it to pulses, a transformer T that transformsthe voltage based on the number of turns n, rectifying transistors Q5and Q6 and resistors R_(Q5) and R_(Q6) that rectify the secondary-sidevoltage of the transformer T and inductor Lo and capacitor Co whichperform pulse averaging. The rectifying transistors Q5 and Q6 andresistors R_(Q5) and R_(Q6) constitute a self-driven type rectifyingcircuit. In addition, the resistance r connected in series with thecapacitor Co is the equivalent series resistance (ESR) of the capacitorCo.

[0054] With the main circuit 1 having such a construction, in thefirst-stage converter 2, the input voltage V_(i) is pulsed and the pulsewidth is controlled to the duty ratio D by the switching transistors Q1and Q2 which are switched by the PWM controller and then averaging isperformed by the filter consisting of the inductor Lb′ and capacitor Cb′and thus the intermediate voltage V_(b) is generated.

[0055] Moreover, in the second-stage converter 3, this intermediatevoltage V_(b) is pulsed by the switching transistors Q3 and Q4, thevoltage is transformed based on the number of turns n of the transformerT, it is again averaged by a filter consisting of the inductor Lo andcapacitor Co, and thus the output voltage V_(o) is generated. Thisoutput voltage V_(o) is supplied to the load R.

[0056] Here, the output voltage V_(o) can be adjusted by changing theduty ratio D under PWM control and thus varying the ON time of theswitching transistor Q1. Note that the switching transistors Q3 and Q4contained within the second-stage converter 3 are controlled such thatthe duty cycle of ON/OFF switching is constant.

[0057]FIG. 2 is a waveform chart showing the operation of the maincircuit 1 of the two-stage DC-DC converter shown in FIG. 1, where (a)shows the gate-source voltage V_(gs) of switching transistor Q1, (b)shows the gate-source voltage V_(gs) of switching transistor Q2, (c)shows the current I_(d(Q1)) flowing through switching transistor Q1, (d)shows the current I_(d(Q2)) flowing through switching transistor Q2, (e)shows the gate-source voltage V_(gs(Q3)) of switching transistor Q3, (f)shows the gate-source voltage V_(gs(Q4)) of switching transistor Q4, (g)shows the voltage V_(MT(primary)) of the primary-side coil oftransformer T, (h) shows the current I_(d(Q3)) flowing through switchingtransistor Q3, (i) shows the current I_(d(Q4)) flowing through switchingtransistor Q4, (j) shows the gate-source voltage V_(gs(Q5)) ofrectifying transistor Q5, (k) shows the gate-source voltage V_(gs(Q6))of rectifying transistor Q6, (l) shows the current I_(d(Q5)) flowingthrough switching transistor Q5, (m) shows the current I_(d(Q6)) flowingthrough switching transistor Q6 and (n) shows the output inductorcurrent I_((LO)) of the inductor Lo.

[0058] Here, in the main circuit 1 of a two-stage DC-DC converter,second order delay is typically generated in each of the first-stageconverter 2 and second-stage converter 3, so fourth order delay isgenerated overall.

[0059] We will now validate this fourth order delay by using thestate-space averaging method to find the transfer function of the maincircuit 1.

[0060] In order to simplify, if the second-stage converter 3 operateswith a constant duty ratio D (e.g., D=0.5), then the main circuit 1 canbe represented by the two-stage filter equivalent circuit 4 shown inFIG. 3.

[0061] Here, the inductors Lb, Cb and Vs shown in FIG. 3 can becalculated by the formula $\begin{matrix}{{{Cb} = \frac{{Cb}^{\prime}}{n^{2}}},{{Lb} = \frac{n^{2} \cdot {Lb}^{\prime}}{2^{2}}},{{Vs} = {\frac{Vin}{2} \cdot n}}} & (1)\end{matrix}$

[0062] respectively and converted as secondary-side components.

[0063] In the equivalent circuit 4 shown in FIG. 3, the state variable Xis represented by:

X=[vo, iL, vb, ib].  (2)

[0064] Here, vo, iL, vb and ib are the output voltage and outputinductor current of the second-stage converter 3 and the output voltage(intermediate voltage) and switching current of the first-stageconverter 2, respectively.

[0065] Thereby, the equation of state of the main circuit 1 of thetwo-stage DC-DC converter is represented by: $\begin{matrix}{{\frac{\quad}{t}X} = {{A \cdot X} + {B \cdot {Vs}}}} & (3)\end{matrix}$

[0066] Here, the matrices A and B in equation (3) above are representedrespectively by: $\begin{matrix}{{{A(R)} = \begin{bmatrix}\frac{- 1}{{Co}\left( {R + r} \right)} & \frac{R}{{Co}\left( {R + r} \right)} & 0 & 0 \\\frac{- R}{{Lo}\left( {R + r} \right)} & \frac{{- R} \cdot r}{{Lo}\left( {R + r} \right)} & \frac{1}{Lo} & 0 \\0 & \frac{- 1}{Cb} & 0 & \frac{1}{Cb} \\0 & 0 & \frac{- 1}{Lb} & 0\end{bmatrix}},{{B(d)} = {\begin{bmatrix}0 \\0 \\0 \\\frac{D}{Lb}\end{bmatrix}.}}} & (4)\end{matrix}$

[0067] Based on these state equations (3) and (4), small-signal analysis(dynamic characteristics) is performed.

[0068] Regarding the above equations of state, solving the equation ofstate for infinitesimal changes in the time domain of the state variableX with respect to the duty ratio D and calculating by means of a Laplacetransform gives the following: $\begin{matrix}\begin{matrix}{\frac{\Delta \quad X}{\Delta \quad D} = {\left( {{s1} - A} \right)^{- 1} \cdot \frac{\partial B}{\partial D} \cdot {Vs}}} \\{= {{\frac{Vs}{{Gch}(s)} \cdot \begin{bmatrix}1 \\{\left\{ {{{sCo}\left( {R + r} \right)} + 1} \right\}/R} \\{\left\{ {{s^{2}{{CoLo}\left( {R + r} \right)}} + {s\left( {{rCoR} + {Lo}} \right)} + R} \right\}/R} \\{\left\{ {{s^{3}{{CoCbLo}\left( {R + r} \right)}} + {s^{2}{{Cb}\left( {{rCoR} + {Lo}} \right)}} + {s\left( {{Cor} + {CbR} + {CoR}} \right)} + 1} \right\}/R}\end{bmatrix}}{\begin{matrix}\left. \leftarrow{vo} \right. \\\left. \leftarrow{iL} \right. \\\left. \leftarrow{vb} \right. \\\left. \leftarrow{ib} \right.\end{matrix}.}}}\end{matrix} & (5)\end{matrix}$

[0069] In this equation (5), Gch(s) is represented by: $\begin{matrix}{\begin{matrix}{{{Gch}(s)} = \left\{ {{s^{4} \cdot {{CoLoCbLb}\left( {R + r} \right)}} + {{s^{3} \cdot \left( {{rCoR} + {Lo}} \right)}{CbLb}} +} \right.} \\{\left. {{s^{2} \cdot \left\lbrack {{{CoLo}\left( {R + r} \right)} + {{CoLb}\left( {R + r} \right)} + {CbLbR}} \right\rbrack} + {s \cdot \left( {{rCoR} + {Lo} + {Lb}} \right)} + R} \right\}/R}\end{matrix}.} & (6)\end{matrix}$

[0070] Here, the matrix elements on the right-hand side of equation (6)above correspond to, in order from top to bottom, vo, iL, vb and ib.

[0071] Accordingly, the transfer function Po(s) of the duty ratio D andoutput voltage vo(s), transfer function of the duty ratio D and theoutput inductor current iL(s) of the second-stage converter 3, transferfunction of the duty ratio D and output voltage vb(s) and transferfunction of the duty ratio D and the switching current ib(s) of thefirst-stage converter 2, are respectively represented by:$\begin{matrix}{{{Po}(s)} = {\frac{\Delta \quad {{vo}(s)}}{\Delta \quad D} = {\frac{Vs}{{Gch}(s)} \cdot 1}}} & (7) \\{\frac{\Delta \quad {{iL}(s)}}{\Delta \quad D} = {\frac{Vs}{{Gch}(s)} \cdot {{PiL}(s)}}} & (8) \\{\frac{\Delta \quad {{vb}(s)}}{\Delta \quad D} = {\frac{Vs}{{Gch}(s)} \cdot {{Pb}(s)}}} & (9) \\{\frac{\Delta \quad {{ib}(s)}}{\Delta \quad D} = {\frac{Vs}{{Gch}(s)} \cdot {{Pib}(s)}}} & (10)\end{matrix}$

[0072] Note that here, PiL(s), Pb(s) and Pib(s) are as follows:

PiL(s)={sCo(R+r)+1}/R  (11)

Pb(s)={s ² CoLo(R+r)+s(CoR+Lo)+R}/R  (12)

Pib(s)={s ³ CoCbLo(R+r)+s ² Cb(rCoR+Lo)+s(Cor+CbR+CoR)+1}/R  (13)

[0073] Accordingly, Gch(s) is a fourth order function of s in equation(6) above, so from equation (7), the transfer function Po(s) of the dutyratio D and output voltage vo(s) becomes a fourth order function, andone can see that fourth order delay occurs in the main circuit 1 of atwo-stage DC-DC converter.

[0074] We shall now study the case of using single-loop output voltagefeedback control in order to control the output voltage V_(o) of themain circuit of such a two-stage DC-DC converter to the desired voltagevalue.

[0075]FIG. 4 is a circuit diagram showing a two-stage DC-DC converterthat uses single-loop output voltage feedback control.

[0076] In FIG. 4, the two-stage DC-DC converter 5 has a structureconsisting of the main circuit 1 of the two-stage DC-DC converter shownin FIG. 1 to which is added an error amplifier 6 and PWM controller 7.Here, the error amplifier 6 and PWM controller 7 constitute an outputvoltage feedback-type control circuit for the main circuit 1.

[0077] The aforementioned error amplifier 6 is provided with an erroramp 6 a, and the output voltage V_(o) of the second-stage converter 3 isvoltage-divided among resistors R1 and R2 and provided as input to theinverted input of the error amp 6 a, while the reference voltage V_(REF)is provided as input to the non-inverted input of the error amp 6 a. Inaddition, a resistor R6 and capacitor C6 are connected in parallelbetween the non-inverted input and output of error amp 6 a, and thus theresponse of the error amp 6 a is limited so that the output voltageV_(o) does not undergo abnormal oscillation.

[0078] The aforementioned PWM controller 7 is provided with adifferential amp 7 a, and a triangular wave is input to its invertedinput as a reference signal, while the output signal from theaforementioned error amplifier 6 is input to its non-inverted input.

[0079] With a two-stage DC-DC converter 5 having such a structure, theoutput voltage feedback control system based on the aforementioned erroramplifier 6 and PWM controller 7 constitutes a single loop as shown inFIG. 5, and the transfer function PPo(s) of the overall open loopbecomes $\begin{matrix}{{{PPo}(s)} = {\frac{Vs}{{Gch}(s)} \cdot {FM} \cdot {{{Gvs}(s)}.}}} & (14)\end{matrix}$

[0080] Here, FM is the conversion ratio of the duty ratio D with respectto the input voltage V_(i) of the PWM controller 7 and Gvs(s) is thetransfer function of the error amplifier 6.

[0081] Here follows a study of the first term Vs/Gch(s) on theright-hand side of equation (14) above. Assuming that the denominatorGch(s) is divisible by ω_(α) and ω_(β), this becomes $\begin{matrix}{\frac{1}{{Gch}(s)} = {\frac{1}{\left( {s^{2} + \omega_{\alpha}^{2}} \right)\left( {s^{2} + \omega_{\beta}^{2}} \right)}.}} & (15)\end{matrix}$

[0082] Here, ω_(α) and ω_(β) respectively become: $\begin{matrix}{{\omega_{\alpha} = \sqrt{\frac{b + \sqrt{b^{2} - {4a}}}{2a}}},{\omega_{\beta} = \sqrt{\frac{b - \sqrt{b^{2} - {4a}}}{2a}.}}} & (16)\end{matrix}$

[0083] As is evident from equation (16), taking the resonance point fbof the second-stage converter 3, output filter resonance point fo of thesecond-stage converter 3, and resonance points fbo and fob found bycombining the respective inductors and capacitors to be: $\begin{matrix}{{{fb} = \frac{1}{2\pi \sqrt{LbCb}}},{{fo} = \frac{1}{2\pi \sqrt{LoCo}}},{{fbo} = \frac{1}{2\pi \sqrt{LbCo}}},{{fob} = \frac{1}{2\pi \sqrt{LoCb}}}} & (17)\end{matrix}$

[0084] the resonance points of 1/Gch(s) become values different fromthese reference points fb, fo, fbo and fob.

[0085] As an example, taking:

Lb=0.68 μH,

Cb=128 μF (secondary-side converted value),

Lo=0.15 μH,

Co=235 μF,

[0086] then fb=17 kHz, fo=26.8 kHz, fbo=12.6 kHz, fob=36.2 kHz, and alsoω_(α)/2π=9.6 kHz and ω_(β)/2π=47.2 kHz. When these resonance points aregraphed as shown in FIG. 6, one can see that the new resonance pointsω_(α) and ω_(β) occur on the outside, namely the low-frequency andhigh-frequency sides, of the reference points fb, fo, fbo and fob. Inthis manner, in a two-stage DC-DC converter, the resonance points onlybecome evident with analysis.

[0087] Moreover, if the equivalent series resistance (ESR) of the outputcapacitor is set to r=10 mΩ, then upon finding Bode plots of the gainand phase as a function of frequency in the transfer function PPo(s) ofthe single-loop output voltage feedback control, the Bode plots are asshown in FIG. 7. In FIG. 7, (a) is a Bode plot showing the gain as afunction of frequency, while (b) is a Bode plot showing the phase as afunction of frequency.

[0088] Here, when the frequency response of the error amplifier 6 isadjusted so that the zero-cross frequency for gain becomes 1 kHz, thenthe gain margin at the frequency at which the phase crosses zero degreesis as follows.

[0089] In this case, the phase rotates rapidly at the first resonancepoint (ω_(α)/2π) and crosses zero degrees at approximately 9.6 kHz, sothe gain margin becomes approximately −1 dB. Considering that the gainmargin on the Bode plot is typically set to roughly −20 dB whendesigning the power supply control system, one can see that there isnearly no margin at all. From the above, one can see that the operationof the control system is unstable in the two-stage DC-DC converter 5shown in FIG. 4.

[0090] In this manner, one can see that stabilization of the controlsystem in a two-stage DC-DC converter is difficult when single-loopoutput voltage feedback control is used.

[0091] Here follows a detailed description of a multi-stage DC-DCconverter according to a preferred embodiment of the present invention.

[0092] Note that the embodiment presented below is a preferred specificexample of the present invention to which are applied varioustechnically preferable limitations, but the scope of the presentinvention is in no way limited to these modes unless the followingexplanation explicitly limits the present invention.

[0093]FIG. 8 is a circuit diagram showing the two-stage DC-DC converteraccording to Preferred Embodiment 1 of the present invention. In FIG. 8,a two-stage DC-DC converter 10 comprises: a first-stage non-isolatedconverter 11, a second-stage isolated converter 12, an error amplifier13 and a PWM controller 14.

[0094] The aforementioned first-stage converter 11 is constructed as aso-called “buck” PWM regulation block, consisting of two switchingtransistors (FET) Q1 and Q2 that perform pulse width control byswitching based on the PWM controller 14, an inductor Lb′ and capacitorCb′ that perform pulse averaging and an input capacitor Ci used tostabilize the input voltage V_(i.) Namely, the first-stage converter 11has a structure similar to that of the first-stage converter 2 of thetwo-stage DC-DC converter 5 shown in FIG. 4.

[0095] Moreover, by means of the switching of the aforementioned PWMcontroller 14, the intermediate voltage V_(b) is kept constant despitefluctuations in the input voltage V_(i) and load.

[0096] In addition, the second-stage converter 12 is constructed as aso-called “half bridge” type, consisting of two switching transistors Q3and Q4 that take the intermediate voltage V_(b) from the first-stageconverter 11 and convert it to pulses, a transformer T that transformsthe voltage based on the number of turns n, rectifying transistors Q5and Q6 and resistors R_(12a) and R_(12b) that rectify the secondary-sidevoltage of the transformer T and inductor Lo and capacitor Co whichperform pulse averaging. The rectifying transistors Q5 and Q6 andresistors R_(12a) and R_(12b) constitute a self-driven type rectifyingcircuit. In this manner, the second-stage converter 12 has a structuresimilar to that of the second-stage converter 3 of the DC-DC converter 5shown in FIG. 4.

[0097] The aforementioned error amplifier 13 is provided with an erroramp 13 a, and the output voltage V₀ of the second-stage converter 12 isvoltage-divided among resistors R1 and R2 and provided as input to theinverted input of the error amp 13 a, while the reference voltageV_(REF) is provided as input to the non-inverted input of the error amp13 a. In addition, a resistor R13 and capacitor C13 are connected inparallel between the non-inverted input and output of error amp 13 a,and thus the response of the error amp 13 a is limited so that theoutput voltage V_(o) does not undergo abnormal oscillation. In thismanner, the error amplifier 13 has a structure similar to that of theerror amplifier 6 of the DC-DC converter 5 shown in FIG. 4.

[0098] The aforementioned PWM controller 14 is provided with adifferential amp 14 a, and a triangular wave is input to its invertedinput as a reference signal, while the output signal from theaforementioned error amplifier 13 is input to its non-inverted input.Namely, the PWM controller 14 has a structure similar to that of the PWMcontroller 7 of the DC-DC converter 5 shown in FIG. 4.

[0099] Thereby, the output voltage V₀ of the second-stage converter 12is provided as negative feedback to the PWM controller 14, and basedthereupon, by appropriately varying the duty cycles of switchingtransistors Q1 and Q2 of the first-stage converter 11, the intermediatevoltage V_(b) which is the output of the first-stage converter 11 isadjusted to keep the output voltage V₀ constant. Note that the signal(Q) that controls switching transistor Q1 is not a completelycomplementary signal to the inverted signal ({overscore (Q)}) thatcontrols switching transistor Q2, but rather a stipulated amount of deadtime is inserted. In addition, the switching transistors Q3 and Q4contained in the second-stage converter 12 are controlled such that suchthat the duty cycle of ON/OFF switching is constant.

[0100] The aforementioned structure is similar to that of the two-stageDC-DC converter 5 shown in FIG. 4, but the two-stage DC-DC converter 10according to this embodiment differs from the two-stage DC-DC converter5 shown in FIG. 4 on the following points.

[0101] In the two-stage DC-DC converter 10 according to this embodiment,an operational amplifier 15 is inserted between the error amplifier 13and PWM controller 14. The operational amplifier 15 consists of an opamp 15 a and resistors R3, R4 and R15.

[0102] In this operational amplifier 15, the output signal V_(c) fromthe error amplifier 13 is input to the non-inverted input of the op amp15 a and also the intermediate voltage V_(b) which is the output of thefirst-stage converter 11 is voltage-divided among resistors R3 and R4and provided as input to the inverted input of the op amp 15 a, whileits output is connected to the non-inverted input of the differentialamp 14 a of the PWM controller 14. In addition, the resistor R15 isconnected between the inverted input and output of the op amp 15 a.

[0103] Thereby, the output voltage V_(o) which is the output of thesecond-stage converter 12 and the intermediate voltage V_(b) which isthe output of the first-stage converter 11 are respectively provided asnegative feedback to the non-inverted input of the differential amp 14 aof the PWM controller 14.

[0104] Here, the error amplifier 13, PWM controller 14 and operationalamplifier 15 constitute a control circuit for the main circuitconsisting of the first-stage converter 11 and second-stage converter12.

[0105] Note that as shown in FIG. 9, it is also possible to use theresistors R3 and R4 alone instead of the aforementioned operationalamplifier 15. In this case, in the same manner as in the two-stage DC-DCconverter 5 shown in FIG. 4, the output signal V_(c) of the erroramplifier 13 is supplied to the non-inverted input of the differentialamp 14 a of PWM controller 14, and also, it is sufficient to supply theinverted input of the differential amp 14 a of the PWM controller 14with the voltage found by voltage-dividing the intermediate voltageV_(b) which is the output of the first-stage converter 11 with theresistors R3 and R4, along with a triangular wave as a reference signal.

[0106] The two-stage DC-DC converter 10 according to this embodiment hasthe structure as described above, and its operation is as follows.

[0107] First, under the control of the PWM controller 14, the switchingtransistors Q1 and Q2 contained in the first-stage converter 11 areswitched alternately, and the input voltage V_(i) is thus pulsed andalso pulse-width controlled by the duty ratio D of switching. Thevoltage thus pulsed is averaged by the filter consisting of the inductorLb′ and capacitor Cb′, and the intermediate voltage V_(b) is generated.

[0108] Moreover, in the second-stage converter 12, this intermediatevoltage V_(b) is pulsed by the switching transistors Q3 and Q4, thevoltage is transformed based on the number of turns n of the transformerT, it is further rectified by rectifying transistors Q5 and Q6, and thenagain averaged by a filter consisting of the inductor Lo and capacitorCo, and thus the output voltage V_(o) is generated. As described above,the switching transistors Q3 and Q4 contained within the second-stageconverter 12 are controlled such that the duty cycle of ON/OFF switchingis constant.

[0109] In this case, in the PWM controller 14, the output voltage V_(o)of the second-stage converter 12 is provided as negative feedback viathe error amplifier 13 in an external loop, while the intermediatevoltage V_(b) of the first-stage converter 11 is provided as negativefeedback in an internal loop. Thereby, the PWM controller 14 alternatelyturns ON the switching transistors Q1 and Q2 contained in thefirst-stage converter 11 and appropriately adjusts the duty ratio D ofswitching transistor Q1 based on the output voltage V_(o) andintermediate voltage V_(b), thereby stabilizing the output voltageV_(o).

[0110] Accordingly, as shown in FIG. 10, the output voltage feedbackcontrol system consisting of the aforementioned error amplifier 13 andPWM controller 14 contains an internal loop with a transfer functionΔvb/ΔD of the intermediate voltage V_(b). Accordingly, the overalltransfer function PPb(s) is represented by the following equation:$\begin{matrix}{{{PPb}(s)} = {\frac{Vs}{{Gch}(s)} \cdot \frac{F\quad M}{\underset{\underset{{Internal}\quad {loop}}{}}{1 + {{\frac{{Pb}(s)}{{Gch}(s)} \cdot F}\quad {M \cdot {Vs}}}}} \cdot {{{Gvs}(s)}.}}} & (18)\end{matrix}$

[0111] Here, if the frequency response of the error amplifier 13 isadjusted so that the zero-cross frequency of the gain of theaforementioned transfer function PPb(s) becomes 1 kHz, then the overallBode plot shown in FIG. 11 is obtained. In FIG. 11, (a) is a Bode plotshowing the gain as a function of frequency, while (b) is a Bode plotshowing the phase as a function of frequency.

[0112] As shown in FIG. 11, the frequency at which the phase crosseszero degrees is 17 kHz so one can see that this is shifted toward thehigh-frequency side in comparison to the two-stage DC-DC converter 5shown in FIG. 4. Thus, the gain margin becomes approximately −15 dB, soone can see that in comparison to the gain margin of approximately −1 dBin the two-stage DC-DC converter 5 shown in FIG. 4, a much larger gainmargin is obtained. Thus, the output voltage feedback control stabilizesthe system.

[0113]FIG. 12 is a circuit diagram showing the two-stage DC-DC converteraccording to Preferred Embodiment 2 of the present invention.

[0114] The two-stage DC-DC converter 20 according to this embodiment hasa structure similar to that of the two-stage DC-DC converter 10 shown inFIG. 8, so the same structural elements are given the same symbols andthe explanations thereof are omitted.

[0115] In the two-stage DC-DC converter 20 according to this embodiment,the intermediate voltage V_(b) of the first-stage converter 11 isvoltage-divided among resistors R3 and R4 and provided as input to thenon-inverted input of the differential amp 14 a of the PWM controller14, and thus it is provided as positive feedback to the PWM controller14. This and the fact that no operational amplifier 15 is provided arethe differences from the two-stage DC-DC converter 10 shown in FIG. 8.In the two-stage DC-DC converter 20 according to this embodiment, thecontrol circuit consists of the error amplifier 13, PWM controller 14and resistors R3 and R4.

[0116] With a two-stage DC-DC converter 20 having such a structure, inthe same manner as the two-stage DC-DC converter 10 shown in FIG. 8, theintermediate voltage V_(b) is generated in the first-stage converter 11and the output voltage V_(o) is generated in the second-stage converter12.

[0117] In this case, in the PWM controller 14, the output voltage V_(o)of the second-stage converter 12 is provided as negative feedback viathe error amplifier 13 in an external loop, while the intermediatevoltage V_(b) of the first-stage converter 11 is provided as positivefeedback in an internal loop. Thereby, the PWM controller 14 alternatelyturns ON the switching transistors Q1 and Q2 contained in thefirst-stage converter 11 and appropriately adjusts the duty ratio D ofswitching transistor Q1 based on the output voltage V_(o) andintermediate voltage V_(b), thereby stabilizing the output voltageV_(o).

[0118] Accordingly, as shown in FIG. 13, the output voltage feedbackcontrol system consisting of the aforementioned error amplifier 13 andPWM controller 14 contains an internal loop with a transfer function ofΔvb/ΔD of the intermediate voltage V_(b). Accordingly, the overalltransfer function PTP(s) is represented by the following equation:$\begin{matrix}{{{PTP}(s)} = {\frac{Vs}{{Gch}(s)} \cdot \frac{F\quad M}{\underset{\underset{{Internal}\quad {loop}}{}}{1 - {{\frac{{Pb}(s)}{{Gch}(s)} \cdot {Vs} \cdot F}\quad M}}} \cdot {{{Gvs}(s)}.}}} & (19)\end{matrix}$

[0119] Here, if the frequency response of the error amplifier 13 isadjusted so that the zero-cross frequency of the gain of theaforementioned transfer function PTP(s) becomes 1 kHz, then the overallBode plot shown in FIG. 14 is obtained. In FIG. 14, (a) is a Bode plotshowing the gain as a function of frequency, while (b) is a Bode plotshowing the phase as a function of frequency.

[0120] In this case, since the “−” sign appears in the denominator ofthe second term on the right-hand side of the transfer function PTP(s),among the two resonance points ω_(α)/2π and ω_(β)/2π, one can see thatthe resonance point ω_(α)/2π on the low-frequency side disappears.Accordingly, at the frequency of 30 kHz at which the phase crosses zerodegrees, the gain margin becomes approximately −35 dB, so a much largergain margin is obtained. Thus, the output voltage feedback controlstabilizes the system even further.

[0121]FIG. 15 is a circuit diagram showing the two-stage DC-DC converteraccording to Preferred Embodiment 3 of the present invention.

[0122] The two-stage DC-DC converter 30 according to this embodiment hasa structure similar to that of the two-stage DC-DC converter 10 shown inFIG. 8, so the same structural elements are given the same symbols andthe explanations thereof are omitted.

[0123] In the two-stage DC-DC converter 30 according to this embodiment,a resistor RB for detecting the switching current i_(b) flowing throughthe first-stage converter 11 is added, and thus the current signalV_(ib) detected thereby is input to the inverted input of thedifferential amp 14 a of the PWM controller 14 as a reference signalinstead of the triangular wave. In addition, a resistor R14 is connectedbetween the inverted input and ground potential of the differential amp14 a of PWM controller 14. Moreover, the output signal V_(c) of theerror amplifier 13 is connected directly to the non-inverted input ofthe differential amp 14 a of the PWM controller 14. The operationalamplifier 15 is not provided. On the above points, it has a structuredifferent from that of the two-stage DC-DC converter 10 shown in FIG. 8.In the two-stage DC-DC converter 30 according to this embodiment, thecontrol circuit consists of the error amplifier 13 and PWM controller14.

[0124] With a two-stage DC-DC converter 30 having such a structure, inthe same manner as the two-stage DC-DC converter 10 shown in FIG. 8, theintermediate voltage V_(b) is generated in the first-stage converter 11and the output voltage V_(o) is generated in the second-stage converter12.

[0125] In this case, in the PWM controller 14, the output voltage V_(o)of the second-stage converter 12 is provided as negative feedback viathe error amplifier 13 in an external loop, while the current signalV_(ib) indicating the switching current i_(b) flowing through thefirst-stage converter 11 is provided as feedback in an internal loop.Thereby, the PWM controller 14 alternately turns ON the switchingtransistors Q1 and Q2 contained in the first-stage converter 11 andappropriately adjusts the duty ratio D of switching transistor Q1 basedon the output voltage V_(o) and intermediate voltage V_(b), therebystabilizing the output voltage V_(o).

[0126] Accordingly, as shown in FIG. 16, the output voltage feedbackcontrol system consisting of the aforementioned error amplifier 13 andPWM controller 14 contains an internal loop with a transfer functionΔvb/ΔD of the switching current i_(b). Thus, the overall transferfunction PPib(s) is represented by the following equation:$\begin{matrix}{{{PPib}(s)} = {\frac{Vs}{{Gch}(s)} \cdot \frac{{- F}\quad {MI}}{\underset{\underset{{Internal}\quad {loop}}{}}{1 + {{\frac{{Pb}(s)}{{Gch}(s)} \cdot {Vs} \cdot F}\quad {{MI} \cdot K}}}} \cdot {{{Gvs}(s)}.}}} & (20)\end{matrix}$

[0127] We shall now study the effect of the internal loop in a controlsystem having such a structure.

[0128] For ease of understanding, we shall study the transfer functionPx(s) of the main circuit with the Gvs(s) term in equation (20) aboveomitted (containing the transfer function of the internal loop), below:$\begin{matrix}{{{Px}(s)} = {\frac{Vs}{{Gch}(s)} \cdot {\frac{{- F}\quad {MI}}{\underset{\underset{{Internal}\quad {loop}}{}}{1 + {{\frac{{Pib}(s)}{{Gch}(s)} \cdot {Vs} \cdot F}\quad {{MI} \cdot K}}}}.}}} & (21)\end{matrix}$

[0129] Since the Pib(s) shown in equation (13) is a cubic function of s,so assuming $\begin{matrix}{1{\frac{{Pib}(s)}{{Gch}(s)} \cdot {Vs} \cdot {FMI} \cdot K}} & (22)\end{matrix}$

[0130] equation (21) above can be approximated by $\begin{matrix}{{{Px}(s)} = {{\frac{1}{{Gch}(s)} \cdot \frac{- 1}{\frac{{Pib}(s)}{{Gch}(s)} \cdot K}} = {\frac{- 1}{{{Pib}(s)} \cdot K} = {\frac{- 1}{\left\{ {{s^{3}{{CoCbLo}\left( {R + r} \right)}} + {s^{2}{{Cb}\left( {{rCoR} + {Lo}} \right)}} + {s\left( {{Cor} + {CbR} + {CoR}} \right)} + 1} \right\}/R} \cdot \frac{1}{K}}}}} & (23)\end{matrix}$

[0131] and if r=0, and when represented as $\begin{matrix}{{{Px}(s)} = {\frac{- 1}{{s^{3} \cdot {CoCbLo}} + {s^{2} \cdot \frac{CbLo}{R}} + {s \cdot \left( {{Cb} + {Co}} \right)} + \frac{1}{R}} = {\frac{- 1}{CoCbLo} \cdot \frac{1}{\left( {s + \omega_{\alpha}} \right)\left( {s^{2} + \omega_{\beta}^{2}} \right)}}}} & (24) \\{{\omega_{\alpha} = \frac{1}{CoR}},{\omega_{\beta} = \frac{1}{\sqrt{\frac{CoCb}{{Co} + {Cb}} \cdot {Lo}}}}} & (25)\end{matrix}$

[0132] one can see that this is a combination of the inflection pointsand resonance points.

[0133] Upon calculating ω_(α)/2π and ω₆₂ /2π, $\begin{matrix}{{\frac{\omega_{\alpha}}{2\pi} = {\frac{1}{2{\pi \cdot {CoR}}} = {\frac{1}{2\pi \times 235_{\mu \quad F} \times 1} = 677_{H\quad z}}}},{\frac{\omega_{\beta}}{2\pi} = 45_{k\quad H\quad z}}} & (26)\end{matrix}$

[0134] are obtained.

[0135] Accordingly, in this case, the two resonance points ω_(α)/2π andω_(β)/2π present in single-loop (external-loop) output voltage feedbackcontrol, which is a fourth-order delay system, will vanish, so it willbecome a third-order delay system and thus the operation of the controlsystem will be further stabilized.

[0136] Here, if the frequency response of the error amplifier 13 isadjusted so that the zero-cross frequency of the gain of theaforementioned transfer function PPib(s) becomes 1 kHz, then the overallBode plot shown in FIG. 17 is obtained. In FIG. 17, (a) is a Bode plotshowing the gain as a function of frequency, while (b) is a Bode plotshowing the phase as a function of frequency.

[0137] As shown in FIG. 17, the two resonance points ω_(α)/2π andω_(β)/2π vanish, so at the frequency of 30 kHz at which the phasecrosses zero degrees, the gain margin becomes approximately −50 dB andthus a much larger gain margin is obtained. Accordingly, the outputvoltage feedback control stabilizes the system even further.

[0138]FIG. 18 is a circuit diagram showing the two-stage DC-DC converteraccording to Preferred Embodiment 4 of the present invention.

[0139] The two-stage DC-DC converter 40 according to this embodiment hasa structure similar to that of the two-stage DC-DC converter 10 shown inFIG. 8, so the same structural elements are given the same symbols andthe explanations thereof are omitted.

[0140] In the two-stage DC-DC converter 40 according to this embodiment,a current transformer CT for detecting the inductor current i_(L)flowing through the second-stage converter 12 and a rectifier 12 a thatrectifies the output of the current transformer CT and generates thecurrent signal V_(iL) are added, and thus this current signal V_(iL) isinput to the inverted input of the differential amp 14 a of the PWMcontroller 14 as a reference signal instead of the triangular wave. Inaddition, a resistor R14 is connected between the inverted input andground potential of the differential amp 14 a of PWM controller 14.Moreover, the output signal V_(c) of the error amplifier 13 is connecteddirectly to the non-inverted input of the differential amp 14 a of thePWM controller 14. The operational amplifier 15 is not provided. On theabove points, it has a structure different from that of the two-stageDC-DC converter 10 shown in FIG. 8. In the two-stage stage DC-DCconverter 40 according to this embodiment, the control circuit consistsof the error amplifier 13 and PWM controller 14.

[0141] With a two-stage DC-DC converter 40 having such a structure, inthe same manner as the two-stage DC-DC converter 10 shown in FIG. 8, theintermediate voltage V_(b) is generated in the first-stage converter 11and the output voltage V_(o) is generated in the second-stage converter12.

[0142] In this case, in the PWM controller 14, the output voltage V_(o)of the second-stage converter 12 is provided as negative feedback viathe error amplifier 13 in an external loop, while the current signalV_(iL) indicating the output inductor current i_(L) of the second-stageconverter 12 is provided as feedback in an internal loop. Thereby, thePWM controller 14 alternately turns ON the switching transistors Q1 andQ2 contained in the first-stage converter 11 and appropriately adjuststhe duty ratio D of switching transistor Q1 based on the output voltageV_(o) and intermediate voltage V_(b), thereby stabilizing the outputvoltage V_(o).

[0143] Accordingly, as shown in FIG. 19, the output voltage feedbackcontrol system consisting of the aforementioned error amplifier 13 andPWM controller 14 contains an internal loop with a transfer functionΔiL/ΔD of the output inductor current i_(b). At this time, therelationship between the output inductor current i_(L) and the dutyratio D is given by the aforementioned equation (8), so the overalltransfer function PPiL(s) is represented by the following equation:$\begin{matrix}{{{PPiL}(s)} = {\frac{Vs}{{Gch}(s)} \cdot \frac{{- F}\quad {MI}}{\underset{\underset{{Internal}\quad {loop}}{}}{1 + {{\frac{P_{{iL}{(s)}}}{{Gch}(s)} \cdot {Vs} \cdot F}\quad {MI}}}} \cdot {{{Gvs}(s)}.}}} & (27)\end{matrix}$

[0144] Here, if the frequency response of the error amplifier 13 isadjusted so that the zero-cross frequency of the gain of theaforementioned transfer function PPiL(s) becomes 1 kHz, then the overallBode plot shown in FIG. 20 is obtained. In FIG. 20, (a) is a Bode plotshowing the gain as a function of frequency, while (b) is a Bode plotshowing the phase as a function of frequency.

[0145] In this case, one can see that the phase of the aforementionedtransfer function PTP(s) does not reach zero degrees. Accordingly, thismeans that the phase does not reach zero degrees so the control systemis constantly stabilized.

[0146] As explained in the foregoing, with the present invention, theoutput voltage of the second-stage converter is provided as negativefeedback to the PWM controller via an external loop, and also theintermediate voltage of the first-stage converter is provided aspositive feedback via an internal loop, or the switching current of thefirst-stage converter or current flowing through the second-stageconverter is provided as feedback.

[0147] Thereby, in comparison to the case of an external loop alone, theresonance frequency on the low-frequency side in the transfer functionfor the entire control system is shifted to a higher frequency orvanishes, and accordingly, the frequency at which the phase crosses zerodegrees also becomes higher or it no longer crosses zero degrees.Accordingly, the gain margin is increased and the operation of thecontrol system is stabilized.

[0148] The present invention is in no way limited to the aforementionedembodiments, but rather various modifications are possible within thescope of the invention as recited in the claims, and naturally thesemodifications are included within the scope of the invention.

[0149] For example, in the various embodiments described above, a bucktype is used as the first-stage converter 11 and a half-bridge type isused as the second-stage converter 12, but this is not a limitation, asit is clear that a boost type or buck-boost type may be used as thefirst-stage converter 11 and a full-bridge type or push-pull type may beused as the second-stage converter 12.

[0150] In addition, the present invention was described in theaforementioned various embodiments using a two-stage DC-DC converter asan example, but the object of the present invention is not limitedthereto, but rather the present invention may also be applied to a DC-DCconverter formed by connecting three or more converters in series.

1. A multi-stage DC-DC converter comprising: a non-isolated DC-DCconverter that is able to adjust an intermediate voltage by PWM controlas a first-stage converter; an isolated DC-DC converter as asecond-stage converter; and a PWM controller that controls a duty cycleof switching of the first-stage converter by means of negative feedbackof an output voltage of the second-stage converter, the intermediatevoltage of the first-stage converter is provided as negative feedback tothe PWM controller.
 2. The multi-stage DC-DC converter as claimed inclaim 1, wherein the intermediate voltage is provided as negativefeedback to the PWM controller via an operational amplifier.
 3. Amulti-stage DC-DC converter configured as a two-stage DC-DC convertercomprising: a non-isolated DC-DC converter that is able to adjust anintermediate voltage by PWM control as a first-stage converter; anisolated DC-DC converter as a second-stage converter; and a PWMcontroller that controls a duty cycle of switching of the first-stageconverter by means of negative feedback of an output voltage of thesecond-stage converter, the intermediate voltage of the first-stageconverter is provided as positive feedback to the PWM controller.
 4. Amulti-stage DC-DC converter configured as a two-stage DC-DC convertercomprising: a non-isolated DC-DC converter that is able to adjust anintermediate voltage by PWM control as a first-stage converter; anisolated DC-DC converter as a second-stage converter; and a PWMcontroller that controls a duty cycle of switching of the first-stageconverter by means of negative feedback of an output voltage of thesecond-stage converter, a switching current of the first-stage converteris provided as feedback to the PWM controller.
 5. A multi-stage DC-DCconverter configured as a two-stage DC-DC converter comprising: anon-isolated DC-DC converter that is able to adjust an intermediatevoltage by PWM control as a first-stage converter; an isolated DC-DCconverter as a second-stage converter; and a PWM controller thatcontrols a duty cycle of switching of the first-stage converter by meansof negative feedback of an output voltage of the second-stage converter,a current flowing through the second-stage converter is provided asfeedback to the PWM controller.
 6. A multi-stage DC-DC convertercomprising: a first DC-DC converter; a second DC-DC converter providedas a latter stage to the first DC-DC converter; and a control circuitthat controls a switching operation performed by the first DC-DCconverter based on at least an output voltage of the first DC-DCconverter and an output voltage of the second DC-DC converter.
 7. Themulti-stage DC-DC converter as claimed in claim 6, wherein the controlcircuit comprises: a first signal generation circuit that generates afirst control signal based on the output voltage of the second DC-DCconverter; a second signal generation circuit that generates a secondcontrol signal based on the output voltage of the first DC-DC converterand the first control signal; and a controller that controls theswitching operation performed by the first DC-DC converter based on thesecond control signal.
 8. The multi-stage DC-DC converter as claimed inclaim 7, wherein the first signal generation circuit compares the outputvoltage of the DC-DC converter against a reference voltage and generatesthe first control circuit based thereupon.
 9. The multi-stage DC-DCconverter as claimed in claim 8, wherein the controller performs PWMcontrol of switch elements contained in the first DC-DC converter basedon the second control signal.
 10. The multi-stage DC-DC converter asclaimed in claim 6, wherein the first DC-DC converter is a non-isolatedDC-DC converter and the second DC-DC converter is an isolated DC-DCconverter.
 11. The multi-stage DC-DC converter as claimed in claim 10,wherein the first DC-DC converter is a buck DC-DC converter and thesecond DC-DC converter is a half-bridge DC-DC converter.
 12. Amulti-stage DC-DC converter comprising: a first DC-DC converter; asecond DC-DC converter provided as a latter stage to the first DC-DCconverter; and a control circuit that controls a switching operationperformed by the first DC-DC converter based on at least one of acurrent flowing through the first DC-DC converter and a current flowingthrough the second DC-DC converter, and an output voltage of the secondDC-DC converter.
 13. The multi-stage DC-DC converter as claimed in claim12, wherein the control circuit comprises: a signal generation circuitthat compares the output voltage of said second DC-DC converter againsta reference voltage and generates a control signal based thereupon; anda controller that controls the switching operation performed by thefirst DC-DC converter based on the control signal and at least one ofthe current flowing through the first DC-DC converter and the currentflowing through the second DC-DC converter.
 14. The multi-stage DC-DCconverter as claimed in claim 13, wherein the controller performs PWMcontrol of switch elements contained in the first DC-DC converter basedon the control signal and at least one of the current flowing throughthe first DC-DC converter and the current flowing through the secondDC-DC converter.
 15. The multi-stage DC-DC converter as claimed in claim12, wherein the first DC-DC converter is a non-isolated DC-DC converterand the second DC-DC converter is an isolated DC-DC converter.
 16. Themulti-stage DC-DC converter as claimed in claim 15, wherein the firstDC-DC converter is a buck DC-DC converter and the second DC-DC converteris a half-bridge DC-DC converter.